The Montgomery County Council, taking a rare hard line with its public employee unions, tentatively agreed Monday to trim negotiated pay increases for county workers and approved a record $2.4 billion schools appropriation, on condition that the Board of Education reduces teacher pay hikes and uses the extra money to pare class size and upgrade instruction.

The council’s actions represent a bid to soften the blow of two major tax increases built into the proposed county operating budget for the fiscal year that begins July 1: a property tax hike of 6 to 9 percent and a rise in taxes on home sales that will increase closing costs.

A final vote on the $5.1 billion spending plan is scheduled for May 26.

The reductions also mark an unusual collaboration between the council and the school board, two bodies that have traditionally clashed over spending. The council signs off on the school’s budget but has no direct control over how the Board of Education spends the money allocated. Over the years, council members have expressed frustration about some of the board’s spending decisions.

Last month, the council told the school board that an 8 percent increase due to teachers, administrators and support staff over the next year under the terms of collective bargaining agreements could not be justified, given the challenges facing the 156,000-student system. Those include ­severe overcrowding and the achievement gaps separating white and Asian students from black and Latino students.

Council concerns about the long-term health of the system led to a 2017 appropriation that is $90 million above the minimum annual spending required by state law. In exchange for the hefty increase, however, the council said it wants raises cut by about half and the money redirected to pressing needs.

The Board of Education has been in discussions with its unions — the Montgomery County Education Association (MCEA), Service Employees International Union Local 500 and the Montgomery County Association of Administrators and Principals — but an accord has not been reached.

Montgomery teachers make an average salary of $76,000. After several years with no raises during the recession, pay has grown 25 to 30 percent from 2010 to 2016, according to an analysis by council staff. The pay is in part a reflection of the MCEA’s clout in local politics. Its “Apple Ballot” of endorsed candidates is mailed to Democratic voters and distributed at polls.

The game-changing development came Friday, when board President Michael A. Durso told the council in a letter that the board is committed to cutting the 8 percent raise roughly in half, “even absent union agreement.” State law allows the board to unilaterally impose contract terms under certain conditions.

Such a cut would free up $36 million to $37 million, which could reduce class size by an average of two students — to the level that existed in 2009.

MCEA President Christopher Lloyd said Monday that the unions will continue discussions with the board.

“Clearly we’ve got to continue to work with the board now about monetary and non-monetary issues,” Lloyd said.

The council has been similarly generous since the recession with unions representing police, fire and non-uniformed employees, which provide money and, in some cases, boots on the ground for campaigns. The contracts were negotiated by County Executive Isiah Leggett (D).

Pay has grown 25 to 30 percent from 2010 to 2016 according to the council analysis.

But last month, the council rejected new contracts to raise pay about 8 percent for members of the Fraternal Order of the Police Lodge 35, the International Association of Firefighters Local 1664 and United Food and Commercial Workers Local 1994 MCGEO (Municipal and County Government Employees Organization). The council members said they wanted the pacts cut to 4.5 percent in parity with the teachers.

The contracts were returned to Leggett, who had 10 days to renegotiate them with the unions. He returned them to the council last week with the increases not cut but shifted nearly entirely toward the next fiscal year. Council staff said the move would result in just $115,485 to be paid in salary increases for fiscal 2017 but $6.8 million devoted to raises in 2018.

Council members expressed regret about having to trim agreed-upon pay packages but said they believed the school system was at a tipping point.

“Unless we made a bold decision this year to infuse these resources . . . we would experience a sliding back,” said council member Nancy Navarro (D-Mid-County).

Council members also said that the school board’s resolve to reduce salaries would not have been possible without the decision to address contracts with police, fire and non-uniformed employees.

“This has not been easy,” council President Nancy Floreen (D-At Large) said. “This has not been an easy lift for everyone involved.”

Union members expressed anger not only about the reductions but their treatment at the council hearing. Prior to the vote, council member Marc Elrich (D-At Large) asked that the council hear from union leaders who were present. But the request was rebuffed by Floreen.

“Totally out of line, totally unacceptable,” Jeff Buddle, president of the firefighters’ union Local 1664, said.